Affiliation:
1. Leiden Institute of Advanced Computer Science
2. Technische Universität Braunschweig
3. Radboud University Nijmegen
Abstract
Coalgebras provide a uniform framework for studying dynamical systems, including several types of automata. In this article, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are sound and complete with respect to behavioral equivalence can be extended to a coarser coalgebraic language equivalence, which arises from a generalized powerset construction that determinizes coalgebras. We show that soundness and completeness are established by proving that expressions modulo axioms of a calculus form the rational fixpoint of the given type functor. Our main result is that the rational fixpoint of the functor
FT
, where
T
is a monad describing the branching of the systems (e.g., non-determinism, weights, probability, etc.), has as a quotient the rational fixpoint of the determinized type functor
F
, a lifting of
F
to the category of
T
-algebras. We apply our framework to the concrete example of weighted automata, for which we present a new sound and complete calculus for weighted language equivalence. As a special case, we obtain nondeterministic automata in which we recover Rabinovich’s sound and complete calculus for language equivalence.
Funder
Fundação para a Ciência e a Tecnologia
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Reference55 articles.
1. Adámek J. and Rosický J. 1994. Locally Presentable and Accessible Categories. Cambridge University Press. Adámek J. and Rosický J. 1994. Locally Presentable and Accessible Categories . Cambridge University Press.
2. Free iterative theories: a coalgebraic view
3. Iterative algebras at work
4. Adámek J. Herrlich H. and Strecker G. E. 2009. Abstract and Concrete Categories: The Joy of Cats 2nd Ed. Dover Publications Mineola NY. Adámek J. Herrlich H. and Strecker G. E. 2009. Abstract and Concrete Categories: The Joy of Cats 2nd Ed. Dover Publications Mineola NY.
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